I was explaining how the NFL draft works basically from scratch to an econ PhD student, let's call him Sam. At first Sam thought that teams bid for the players much like free agency. I explained that teams select players and then have the exclusive rights to sign them to a contract for the next year. Sam had big misgivings about this structure. His complaint was that this gives so much power to the teams and that they would be able to get a very good deal since the player has no outside options besides waiting a year and re-entering the draft (where the player would be drafted in a later round and would have a lower expected payoff).
It took me a little while to reconcile why this doesn't happen. Top picks in the draft are generally believed to be overpaid in comparison to what they would be paid in a free agency model. This must mean that the players have much more power than the teams, especially for early draft picks. I resolved this by realizing that the role of agents is more than just understanding the legal intricacies of the contracts. Agents, and the agency problem that ensues, are used by college players entering the draft as a commitment device to reject low offers.
Suppose that Sam Bradford, the consensus number one pick this year had no agent. He would be picked first by the St. Louis Rams, but both the Rams and Bradford would know that if Bradford did not sign, he would have to enter the draft again next year, and after a year of not playing, he would be drafted much lower, maybe at the 10th pick. Suppose the 10th pick usually gets paid half as much as the first pick. Bradford can not credibly threaten not to sign for a low amount if it is higher than what he would get had he been drafted at number 10. The teams can credibly threaten not to raise their offer since they are in a repeated game with draft picks every year, while Bradford is in a single shot game.
But the agents change the game. The agents have an agency problem, which actually serves to benefit the player. While the player can not credibly threaten to not accept an offer higher than his reservation wage, the agent can credibly threaten not to accept an offer higher than the player's reservation wage. This is because the agent is also in a repeated game. If Sam Bradford's agent accepts a deal which is 20% lower than the deal the first pick got last year, he will never work again. So teams know that the agent needs to get a decent deal (relative to past deals).
If the teams try to lowball the offer and the agent refuses and the player enters the draft the next year, this is very bad for the player, but it is not very bad for the agent. The agent gains a reputation for refusing lowball offers, which makes him even more likely to be hired by future college players.
In an ultimatum game setting, suppose the person receiving the offer was allowed to hire an agent to make his decisions and that this agent was a public figure with a reputation. Which agents would be most desirable from the receiver's perspective? They would be the agents who have a reputation for rejecting any offer less than 95% of the total pool. This threat is credible to the person making the offer in the ultimatum game since the agent has a reputation that is valuable to him and would be destroyed by accepting a low offer. So the ability of players in the ultimatum game to hire publicly known agents completely reverses the power each player has in the game, and shifts the rational equilibrium from the offering player extracting most of the surplus to the receiving player extracting most of the surplus. The agents, and the agency problem, act as a commitment device which benefits the players hiring the agents.